One synonym for "injuring reputation" is "defaming." Defaming means to harm someone's reputation through false or damaging statements. Another synonym could be "slandering," which is making false statements about someone with the intent to harm their reputation. A third synonym for "injuring reputation" is "besmirching," which means to tarnish or sully someone's reputation or good name. "Dishonoring" is also a synonym, which means to cause someone to lose respect or reputation through shameful or disreputable behavior. Lastly, "disparaging" is another synonym for "injuring reputation" which means to belittle or speak negatively about someone in a way that harms their reputation.